Advanced statistical methods

Michal Jurajda

Statistics

• What is statistics?

Statistics

• What is statistics good for?

• Mass phenomenons/random events– Data management– Data description– Data analysis

• Statistics helps us to cope with variability of the world we live in.

Statistics

• Decision making.

• Statistics helps us to separate real effects from effects of random variation.

Statistics

• Descriptive statistics

Statistics

• Statistical induction– Drawing conclusions about population from

the sample.– SE standard error SE=SD/√n – CI confidence interval 95%

sample mean ± 1,96 SE

Statistics

• Hypotheses testing– Comparing two independent samples– Comparing two dependent variables

– Paired/non-paired tests

– Parametric/non-parametric tests

Statistics

• p value

• What the p-value tells to us? (type I error).

Frequency tables

• Chi-square test

• Fischer exact test

Normality testing

• Kolmogorov-Smirnov test

• Shapiro-Wilk

Multiple samples

• Multiple comparison procedures– ANOVA– Holm‘s test, Bonferoni method

• p/number of comparisons

– Non-parametric test: Kruskal-Wallis ANOVA

Survival analysis

• Kaplan Meier‘s curves– comparison: log rank test

Logistic regresion

• Binary response variable (death/survival or healty/diseased) is related to „explanatory“ variable. Explanatory variable is continuous or categorial.

Cluster analysis